Conventional electronic circuits for RF and telecommunications applications comprise one or more input ports to which input RF signals of the electronic circuit are fed, and one or more output ports from which output RF signals of the electronic circuit are emitted. Single-ended input/output ports have a pair of connection terminals: a signal terminal and a ground terminal, where the input and output RF signals of the electronic circuit are carried on the signal terminal and where the ground terminal provides a reference against which the RF signal on the signal terminal is defined.
In RF and telecommunications applications it is sometimes preferable to employ electronic circuits where the input/output (hereinafter referred to as I/O) ports of the device comprise a pair of signal carrying terminals where each terminal carries part of an input or output electrical signal of the electronic circuit.
The pair of RF signals carried on each terminal described above can be individually referenced to ground, or can be described mathematically as a linear combination of two signals: a differential mode signal and a common mode signal. A differential mode signal is divided between two terminals so that the amplitude of the signal on each terminal is the same, and so that there is a phase difference of 180° between both signals; thus, the two parts of a differential signal carried on a pair of terminals are out of phase. A common mode signal is divided across two terminals so that the amplitude of the signal on each terminal is the same, and so that both signals are in phase; thus, the two parts of a common mode signal carried on a pair of terminals are identical.
Differential mode signals are less susceptible to noise than common mode signals and consequently differential mode signals are often preferred for applications where a very high signal to noise ration is required.
RF circuits comprising a pair of terminals for each I/O port of the circuit are usually designed to process differential signals and are usually referred to as differential circuits. Sometimes RF circuits comprising a pair of terminals for each I/O port of the circuit are referred to as “balanced circuits”.
A procedure for the analysis of differential circuits, differential components and differential devices is outlined by D. E. Brockelman, W. R. Eisenstadt; “Combined Differential and Common-Mode Scattering Parameters: Theory and Simulation”; IEEE Transactions on Microwave Theory and Techniques, Vol. 43, No. 7, July 1995, pp 1530-1539. According to Brockelman, a differential circuit can be evaluated in terms of the single ended s-parameters which are determined at each signal carrying terminal of the circuit or between any pair of signal carrying terminals of the circuit. A linear transform is used to give what are known as the mixed mode s-parameters of the differential circuit.
For an electronic circuit with two differential I/O ports, the mixed mode S-matrix SMM is defined by EQUATION 1.
                              S          MM                =                                            (                                                                                                                                                                                        Differential                                                                                                                                                              Mode                              ⁢                                                                                                                          ⁢                              Stimulous                                                                                                                                                                                                                                                Common                                                                                                                                                              Mode                              ⁢                                                                                                                          ⁢                              Stimulous                                                                                                                                                                                                                                                                                                                  S                                                              DD                                ⁢                                                                                                                                  ⁢                                11                                                                                                                                                                        S                                                              DD                                ⁢                                                                                                                                  ⁢                                12                                                                                                                                                                                                                        S                                                              DD                                ⁢                                                                                                                                  ⁢                                21                                                                                                                                                                        S                                                              DD                                ⁢                                                                                                                                  ⁢                                22                                                                                                                                                                                                                                                                                                            S                                                              D                                ⁢                                                                                                                                  ⁢                                C                                ⁢                                                                                                                                  ⁢                                11                                                                                                                                                                        S                                                              D                                ⁢                                                                                                                                  ⁢                                C                                ⁢                                                                                                                                  ⁢                                12                                                                                                                                                                                                                        S                                                              D                                ⁢                                                                                                                                  ⁢                                C                                ⁢                                                                                                                                  ⁢                                21                                                                                                                                                                        S                                                              D                                ⁢                                                                                                                                  ⁢                                C                                ⁢                                                                                                                                  ⁢                                22                                                                                                                                                                                                                                                                                                                                                S                                                              C                                ⁢                                                                                                                                  ⁢                                D                                ⁢                                                                                                                                  ⁢                                11                                                                                                                                                                        S                                                              C                                ⁢                                                                                                                                  ⁢                                D                                ⁢                                                                                                                                  ⁢                                12                                                                                                                                                                                                                        S                                                              C                                ⁢                                                                                                                                  ⁢                                D                                ⁢                                                                                                                                  ⁢                                21                                                                                                                                                                        S                                                              C                                ⁢                                                                                                                                  ⁢                                D                                ⁢                                                                                                                                  ⁢                                22                                                                                                                                                                                                                                                                                                            S                                                              CC                                ⁢                                                                                                                                  ⁢                                11                                                                                                                                                                        S                                                              CC                                ⁢                                                                                                                                  ⁢                                12                                                                                                                                                                                                                        S                                                              CC                                ⁢                                                                                                                                  ⁢                                21                                                                                                                                                                        S                                                              CC                                ⁢                                                                                                                                  ⁢                                22                                                                                                                                                                                                                                    )                        _                    ⁢                                                                                                                                                                  Differential                                                                                                                                                  Mode                            ⁢                                                                                                                  ⁢                            Response                                                                                                                                                                                                                                                            Common                                                                                                                                                  Mode                            ⁢                                                                                                                  ⁢                            Response                                                                                                                                                          _                        _                                              EQUATION        ⁢                                  ⁢        1            
The linear transformation from the single ended s-parameters to the mixed mode s-parameters for a two port differential circuit is given in EQUATION 2.
                              S          MM                =                  (                                                                                          1                    2                                    ⁢                                      (                                                                  S                        11                                            -                                              S                        12                                            -                                              S                        21                                            +                                              S                        22                                                              )                                                                                                                    1                    2                                    ⁢                                      (                                                                  S                        13                                            -                                              S                        14                                            -                                              S                        23                                            +                                              S                        24                                                              )                                                                                                                    1                    2                                    ⁢                                      (                                                                  S                        11                                            +                                              S                        12                                            -                                              S                        21                                            -                                              S                        22                                                              )                                                                                                                    1                    2                                    ⁢                                      (                                                                  S                        13                                            +                                              S                        14                                            -                                              S                        23                                            -                                              S                        24                                                              )                                                                                                                                            1                    2                                    ⁢                                      (                                                                  S                        31                                            -                                              S                        32                                            -                                              S                        41                                            +                                              S                        42                                                              )                                                                                                                    1                    2                                    ⁢                                      (                                                                  S                        33                                            -                                              S                        34                                            -                                              S                        43                                            +                                              S                        44                                                              )                                                                                                                    1                    2                                    ⁢                                      (                                                                  S                        31                                            +                                              S                        32                                            -                                              S                        41                                            -                                              S                        42                                                              )                                                                                                                    1                    2                                    ⁢                                      (                                                                  S                        33                                            +                                              S                        34                                            -                                              S                        43                                            -                                              S                        44                                                              )                                                                                                                                            1                    2                                    ⁢                                      (                                                                  S                        11                                            -                                              S                        12                                            +                                              S                        21                                            -                                              S                        22                                                              )                                                                                                                    1                    2                                    ⁢                                      (                                                                  S                        13                                            -                                              S                        14                                            +                                              S                        23                                            -                                              S                        24                                                              )                                                                                                                    1                    2                                    ⁢                                      (                                                                  S                        11                                            +                                              S                        12                                            +                                              S                        21                                            +                                              S                        22                                                              )                                                                                                                    1                    2                                    ⁢                                      (                                                                  S                        13                                            +                                              S                        14                                            +                                              S                        23                                            +                                              S                        24                                                              )                                                                                                                                            1                    2                                    ⁢                                      (                                                                  S                        31                                            -                                              S                        32                                            +                                              S                        41                                            -                                              S                        42                                                              )                                                                                                                    1                    2                                    ⁢                                      (                                                                  S                        33                                            -                                              S                        34                                            +                                              S                        43                                            -                                              S                        44                                                              )                                                                                                                    1                    2                                    ⁢                                      (                                                                  S                        31                                            +                                              S                        32                                            +                                              S                        41                                            +                                              S                        42                                                              )                                                                                                                    1                    2                                    ⁢                                      (                                                                  S                        33                                            +                                              S                        34                                            +                                              S                        43                                            +                                              S                        44                                                              )                                                                                )                                    EQUATION        ⁢                                  ⁢        2            
EQUATION 1 shows that a two port differential circuit can be analysed using a similar method to that employed for a two port single-ended circuit, except that for a two port differential circuit of there are four 2×2 matrices of s-parameters instead of one 2×2 matrix due to the fact that the circuit can be driven at port 1 by a differential mode stimulus or a common mode stimulus, and because the response at port 2 can be either a differential mode response or a common mode response.
Differential circuits can be adversely affected if an input signal of the circuit contains a high common mode component. In many cases a differential circuit will pass a common mode signal from the input of the circuit to the output of the circuit; this would be characterized by a large value of SCC21 for the circuit.
Differential circuits which are fed differential input signals sometimes introduce an unwanted common mode component in the output signals; this is referred to as mode conversion, and would be characterized by a large value of the term SCD21 for the circuit.
An ideal differential output circuit will produce output signals which have no common mode component at all; however, an acceptable performance level for most applications is that the common mode component of the output signal is at least 30 dB less than the differential mode component of the output. This performance level is usually only required within the operating band of the differential circuit.
Unfortunately it is often the case that differential circuits produce output signals with a higher ratio of common mode to differential mode than −30 dB.
FIG. 1 shows a block diagram of a differential circuit 10 comprising a pair of differential I/O ports P1, P2, where I/O port P1 comprises a pair of signal carrying terminals T1, T2 and where I/O port P2 comprises a pair of signal carrying terminals T3, T4. A circuit network 12 is connected between I/O port P1 and port and I/O port P2. The electronic circuit 10 is terminated at the I/O port P1 by a source termination 11, which is characterized by a differential mode impedance ZDS and a common mode impedance ZCS, and is terminated at the I/O port P2 by a load termination 13 which is characterized by a differential mode impedance ZDL and a common mode impedance ZCL.
If it is assumed that the differential circuit 10 of FIG. 1 is symmetric about the axis 15, then the following identities apply:S21=S12, S43=S34;S32=S41, S31=S41;S11=S22, S33=S44.
In this case the mixed mode s-matrix of EQUATION 2 can be simplified to that of EQUATION 3.
                              S          MM                =                                            (                                                                                                                                                                                        Differential                                                                                                                                                              Mode                              ⁢                                                                                                                          ⁢                              Stimulous                                                                                                                                                                                                                                                Common                                                                                                                                                              Mode                              ⁢                                                                                                                          ⁢                              Stimulous                                                                                                                                                                                                                                                                                                                  S                                                              DD                                ⁢                                                                                                                                  ⁢                                11                                                                                                                                                                        S                                                              DD                                ⁢                                                                                                                                  ⁢                                12                                                                                                                                                                                                                        S                                                              DD                                ⁢                                                                                                                                  ⁢                                21                                                                                                                                                                        S                                                              DD                                ⁢                                                                                                                                  ⁢                                22                                                                                                                                                                                                                                                                              0                                                                                0                                                                                                                                0                                                                                0                                                                                                                                                                                                                                                        0                                                                                0                                                                                                                                0                                                                                0                                                                                                                                                                                                                                                  S                                                              CC                                ⁢                                                                                                                                  ⁢                                11                                                                                                                                                                        S                                                              CC                                ⁢                                                                                                                                  ⁢                                12                                                                                                                                                                                                                        S                                                              CC                                ⁢                                                                                                                                  ⁢                                21                                                                                                                                                                        S                                                              CC                                ⁢                                                                                                                                  ⁢                                22                                                                                                                                                                                                                                    )                        _                    ⁢                                                                                                                                                                  Differential                                                                                                                                                  Mode                            ⁢                                                                                                                  ⁢                            Response                                                                                                                                                                                                                                                            Common                                                                                                                                                  Mode                            ⁢                                                                                                                  ⁢                            Response                                                                                                                                                          _                        _                                              EQUATION        ⁢                                  ⁢        3            
The differential circuit 10 of FIG. 1 presents a differential mode impedance and a common mode impedance at I/O port P1, and presents a differential mode impedance and a common mode impedance at I/O port P2. If the circuit is assumed to be symmetric as described by EQUATION 3, then the differential mode impedance at I/O port P1 which is represented by ZD1 and the common mode impedance at I/O port P1 which is represented by ZC1 can be defined in terms of the mixed mode s-parameters as follows:
                                          Z                          D              ⁢                                                          ⁢              1                                =                                    Z              DS                        ×                          (                                                1                  +                                      S                                          DD                      ⁢                                                                                          ⁢                      11                                                                                        1                  -                                      S                                          DD                      ⁢                                                                                          ⁢                      11                                                                                  )                                      ⁢                                  ⁢                              Z                          C              ⁢                                                          ⁢              1                                =                                    Z              CS                        ×                          (                                                1                  +                                      S                                          CC                      ⁢                                                                                          ⁢                      11                                                                                        1                  -                                      S                                          CC                      ⁢                                                                                          ⁢                      11                                                                                  )                                                          EQUATION        ⁢                                  ⁢        4                            where ZDS, ZCS are the respective differential mode and common mode impedances of the source 11.        
Similarly the differential mode impedance at I/O port P2 ZD2 and the common mode impedance at I/O port P2 ZC2 are defined in terms of the mixed mode s-parameters as follows:
                                          Z                          D              ⁢                                                          ⁢              2                                =                                    Z              DL                        ×                          (                                                1                  +                                      S                                          DD                      ⁢                                                                                          ⁢                      22                                                                                        1                  -                                      S                                          DD                      ⁢                                                                                          ⁢                      22                                                                                  )                                      ⁢                                  ⁢                              Z                          C              ⁢                                                          ⁢              2                                =                                    Z              CL                        ×                          (                                                1                  +                                      S                                          CC                      ⁢                                                                                          ⁢                      22                                                                                        1                  -                                      S                                          CC                      ⁢                                                                                          ⁢                      22                                                                                  )                                                          EQUATION        ⁢                                  ⁢        5                            where ZDL, ZCL are the respective differential mode and common mode impedances of the load 13.        
It can be seen from equations 4 and 5 that the differential mode impedance presented by I/O port P1 of the differential circuit 10 is matched to the differential mode impedance ZDS of the source 11 and that the differential mode impedance presented by I/O port P2 of the differential circuit 10 is matched to the differential mode impedance ZDL of the load 13 when the relationships of EQUATION 6 apply.SDD11=0→ZD1=ZDSSDD22=0→ZD2=ZDL  EQUATION 6
If EQUATION 6 applies, and if the circuit of FIG. 1 is lossless, differential mode signals which are incident on I/O port P1 will be passed without attenuation to I/O port P2 and differential mode signals which are incident on I/O port P2 will be passed without attenuation to I/O port P1.
The circuit of FIG. 1 will block common mode signals from being transmitted from I/O port P1 to I/O port P2 (and vice versa) when the common mode impedances at ports P1 and P2 are respectively zero Ω.
It can also be seen from equations 4 and 5, that the common mode impedances presented by I/O ports P1 and P2 of the differential circuit 10 become zero under the following conditions.SCC11=−1→ZC1=0SCC22=−1→ZC2=0  EQUATION 7
For a lossless device, the scalar product of any rows or columns of the s-matrix must be unity. Combining this property with EQUATION 3, EQUATION 6 and EQUATION 7 gives the following mixed mode s-matrix for a two port differential circuit which passes the differential mode component of a signal incident on an input port of the circuit to an output port of the circuit without attenuation, and which presents a common mode impedance of zero Ω to a signal incident on an input port of the circuit, thereby blocking the common mode component of the signal from an output port of the circuit.
                              S          MM                =                                            (                                                                                                                                                                                        Differential                                                                                                                                                              Mode                              ⁢                                                                                                                          ⁢                              Stimulous                                                                                                                                                                                                                                                Common                                                                                                                                                              Mode                              ⁢                                                                                                                          ⁢                              Stimulous                                                                                                                                                                                                                                                                                    0                                                                                1                                                                                                                                1                                                                                0                                                                                                                                                                                                                    0                                                                                0                                                                                                                                0                                                                                0                                                                                                                                                                                                                                                        0                                                                                0                                                                                                                                0                                                                                0                                                                                                                                                                                                                                                  -                              1                                                                                                            0                                                                                                                                0                                                                                                              -                              1                                                                                                                                                                                                      )                        _                    ⁢                                                                                                                                                                  Differential                                                                                                                                                  Mode                            ⁢                                                                                                                  ⁢                            Response                                                                                                                                                                                                                                                            Common                                                                                                                                                  Mode                            ⁢                                                                                                                  ⁢                            Response                                                                                                                                                          _                        _                                              EQUATION        ⁢                                  ⁢        8            
From EQUATION 1, the corresponding single-ended S matrix can be derived.
                              S          SE                =                  (                                                                                                                                        -                        1                                            /                      2                                                                                                                          -                        1                                            /                      2                                                                                                                          +                        1                                            /                      2                                                                                                                          -                        1                                            /                      2                                                                                                                                                          -                        1                                            /                      2                                                                                                                          -                        1                                            /                      2                                                                                                                          -                        1                                            /                      2                                                                                                                          +                        1                                            /                      2                                                                                                                                                          +                        1                                            /                      2                                                                                                                          -                        1                                            /                      2                                                                                                                          -                        1                                            /                      2                                                                                                                          -                        1                                            /                      2                                                                                                                                                          -                        1                                            /                      2                                                                                                                          +                        1                                            /                      2                                                                                                                          -                        1                                            /                      2                                                                                                                          -                        1                                            /                      2                                                                                  _                        _                    )                                    EQUATION        ⁢                                  ⁢        9            
Thus the required properties of a two port differential circuit which passes a differential signal incident on an input port of the circuit without attenuation to an output port of the circuit and which blocks a common mode signal which is incident on an input port of the circuit thereby preventing the common mode signal from being passed to an output port of the circuit are given in EQUATIONS 6 and 7, and the corresponding s-matrices are given in EQUATION 8 and 9.
FIG. 2 shows a block diagram of an electronic circuit 20 comprising a first differential I/O port P1, and a second differential I/O port P2, where the first differential I/O port P1 comprises a pair of signal carrying terminals T1 and T2, and where the second differential I/O port P2 comprises a pair of signal carrying terminals T3 and T4. A transmission line element 24 is arranged so that a first end of the transmission line element 24 is connected to a first circuit node 23A, and so that a second end of the transmission line element 24 is connected to a second circuit node 23B. Signal carrying terminals T1 and T3 are connected to first circuit node 23A and signal carrying terminals T2 and T4 are connected to second circuit node 23B. The electronic circuit has a given operating band defined by a lower frequency limit FL and an upper frequency limit FU. The transmission line element has an electrical length E which is equal to 180° (one half wavelength) at the centre of the operating band of the electronic circuit
The same circuit is depicted in FIG. 7 of U.S. Pat. No. 6,900,705, Nakamura.
The circuit of FIG. 2 has the required electrical properties when the source impedance is equal to the load impedance, i.e. the differential mode component of an electrical signal incident on I/O port P1 is passed substantially without attenuation to I/O port P2 of the electronic circuit, and the common mode component of the impedance of I/O port P1 of the electronic circuit is zero Ω, so that the common mode component of an electrical signal incident on I/O port P1 is blocked from I/O port P2; similarly the differential mode component of an RF signal incident on I/O port P2 is passed substantially without attenuation to I/O port P1, and the common mode component of the impedance of I/O port P2 of the electronic circuit is zero Q, so that the common mode component of an RF signal incident on I/O port P2 is blocked from I/O port P1.
Despite having the required electrical properties, the circuit of FIG. 2 is impractical for use in miniaturized electronic appliances such as portable cellular handsets or W-LAN modules due to the very large physical dimensions of the half wavelength transmission line 24. For example, at an operating frequency of 2.45 GHz, the centre of the band specified in IEEE 802.11b/g for W-LAN applications, a half wavelength transmission line will have a length of 61.22 mm in air and will have an electrical length given by the expression below for a transmission line fabricated in a dielectric material.
                    λ        2                          f      =              2.45        ⁢                                  ⁢        GHz              =            61.22                        ɛ          r                      ⁢                  ⁢    mm                  where εr is the relative dielectric constant of the material.        
Nakamura describes a number of two port differential circuits for attenuating the common mode component of a signal incident on an input port of the circuit comprising multiple discrete components (FIGS. 8, 9 10, 11, 12, 13). However, each of the embodiments described in Nakamura suffer from two drawbacks.
The first drawback is that in order that each of the circuits have the required electrical properties, i.e. that the common mode impedance is zero within the operating band of the circuit, and that the differential mode impedance is matched to the termination at the source or the load of the component, two of the component values must become infinitely large. For example in FIG. 9, the values of capacitors Cg1 and Cg2 must approach infinity in order to reduce the common mode impedance of the circuit to zero, and moreover increasing the capacitance of capacitors Cg1 and Cg2 to sufficiently large values requires that the inductance of inductor Lb become impractically small.
Similarly in FIG. 10 of Nakamura the values of inductors Lg1 and Lg2 become infinitely large in order that the differential mode impedance presented by the circuit is matched to the termination at the source or the load. This reduced the required capacitance of capacitor Cb so that it becomes infinitesimally small.
FIG. 3 shows a two port differential circuit 30 for attenuating the common mode component of a signal incident on an I/O port P1 or P2 of the circuit where the circuit comprises a PI-type discrete circuit connected in parallel with the I/O port P1 and connected in parallel with the I/O port P2 of the circuit similar to the circuit of Nakamura FIG. 9. The PI-type discrete circuit comprises shunt capacitors 36A, 36B, and series inductor 38. FIG. 4A shows the differential mode reflection coefficient (SDD11) and the common mode reflection co-efficient (SCC11) of the circuit of FIG. 3 plotted on a Smith chart for the case where the capacitances of capacitors 36A and 36B are both 10 pF and for the case where the differential mode impedances of the source and load are both 100Ω. The resulting common mode impedance at 2.45 GHz is 25×(0.0166−j0.1278)Ω, and the required inductance of inductor 38 so that the differential mode impedance of the circuit 30 is matched to the source at I/O port P1 and is matched to the load at I/O port P2 is 0.422 nH at an operating frequency of 2.45 GHz.
FIG. 4B shows a plot of the differential mode response (SDD21) and the common mode response (SCC21) of the circuit of FIG. 3 for the case where the capacitances of capacitors 36A and 36B are both 10 pF as described above. The differential mode insertion loss in the frequency range from 2.4 GHz to 2.5 GHz is less than 0.2 dB which is a good result; however, the minimum common mode rejection of the circuit in the frequency range from 2.4 GHz to 2.5 GHz is 12 dB approximately; this is not sufficiently high for typical RF applications.
FIG. 4C shows a Smith chart plot of the differential mode reflection coefficient (SDD11) and the common mode reflection co-efficient (SCC11) of the circuit of FIG. 3 for the case where the capacitances of capacitors 36A and 36B are both 20 pF. The resulting common mode impedance at 2.45 GHz is 25×(0.0042−j0.0647)Ω, and the required inductance of inductor 38 so that the differential mode impedance is matched to the source at I/O port P1 and is matched to the load at I/O port P2 (100 Ohms) is 0.211 nH at an operating frequency of 2.45 GHz. Such a small inductance is very difficult to consistently realize in a mass production environment.
The second drawback of each of the circuits described in FIGS. 8, 9, 10, 11 and 12 of Nakamura is that they all require at least one inductive element. Unfortunately, if the circuit is to be fabricated using multilayer technology employing materials with a high dielectric constant, such as low temperature co-fired ceramic (LTCC), the realization of high Q inductors is difficult, and the insertion loss of the circuit becomes high.
For example multilayer LTCC substrates with a layer thickness of 40 μm and a dielectric constant of 75 are typical for RF applications at 2.45 GHz. The resulting capacitance between mutual windings of an inductor is sufficiently large to lower the self resonant frequency of the inductor to a frequency well below 2.45 GHz.
Other prior art solutions for attenuating a common mode component of an RF signal such as U.S. Pat. No. 6,940,369; “Surface acoustic wave device having excellent balancing characteristics between balanced terminals and a communication device using the same”, Nakahashi, and U.S. Pat. No. 6,919,781: “Surface wave filter comprising reactance elements”, Baier, deal with specific topologies for acoustic filters, and hence cannot be used in the general case where a circuit is required which has the function of passing a differential mode component of an RF signal and blocking a common mode component of the same signal.